Poincaré–Bendixson index theorem showed that: if planar smooth differential systems have
only finitely number of singular points inside a limit cycle, then the sum of the indices at …

Constraints are ubiquitous when studying mechanical systems and fall into two main
categories: hybrid (1-sided, unilateral) and nonholonomic/holonomic (2-sided, bilateral) …

The topological index, or simply the index, of an equilibrium point of a vector field is an
integer which saves important information about the local phase portrait of the equilibrium …

Some aspects concerning chaos and minimal sets in discontinuous dynamical systems are
addressed. The orientability dependence of trajectories sliding trough some variety is …

This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4339749
Page 1 1 ON THE POINCARÉ INDEX FORMULA FOR PLANAR PIECEWISE SMOOTH …

Recentemente, a teoria sobre campos vetoriais suaves por partes (CVSPs) tem passado por
importantes desenvolvimentos. Uma linha de investigação desses campos vetoriais é …

Despite of the fact that piecewise smooth vector fields have been used to model a large
range of physical phenomena and other applications, there exists nowadays an evident lack …